7.6: Chapter 7 - Key Terms and Symbols

Key Terms

Confidence Interval: An interval estimate that gives a range of values likely to contain the population parameter with a certain level of confidence.

Confidence Level: The probability that the confidence interval contains the true population parameter; common levels are 90%, 95%, and 99%.

Margin of Error: The maximum expected difference between the point estimate and the actual population parameter; it reflects the precision of the estimate.

Point Estimate: A single value derived from sample data used to estimate a population parameter.

Population Mean: The average value of a characteristic for the entire population.

Population Proportion: The ratio of individuals in a population with a particular characteristic, expressed as a decimal or percent.

Proportion Complement: The value obtained by subtracting the sample or population proportion from 1; represents the opposite category.

Sample Mean: The average value of a characteristic in a sample, used as a point estimate for the population mean.

Sample Proportion: The ratio of individuals in a sample with a particular characteristic.

Sample Size: The number of observations or data points in a sample affects the accuracy and reliability of confidence intervals.

Sampling Distribution: The probability distribution of a statistic (like the sample mean or proportion) based on all possible random samples from a population.

Sampling Error: The difference between the sample statistic and the corresponding population parameter due to chance variation in sample selection.

Standard Error: A measure of the variability of a sampling distribution; it is used to construct confidence intervals.

t-Distribution: A probability distribution used instead of the normal distribution when estimating the population mean with a small sample size or when the population standard deviation is unknown.

z-Value (or z-Score): A value from the standard normal distribution used in constructing confidence intervals when the population standard deviation is known and the sample size is large.

Key Symbols

\( \bar{x} \) - sample mean.

\( \mu \) - population mean.

\( \hat{p} \) - sample proportion.

\( p \) - population proportion.

\( q \) - complement of the population proportion (i.e., \( q = 1 - p \)).

\( \hat{q} \) - complement of the sample proportion (i.e., \( \hat{q} = 1 - \hat{p} \)).

\( n \) - sample size.

\( E \) - margin of error.

\( \alpha \) - significance level (i.e., \( 1 - \) confidence level).

\( z_{\alpha/2} \) - critical value from the standard normal distribution.

\( t_{\alpha/2} \) - critical value from the t-distribution.

\( \sigma \) - population standard deviation.

\( s \) - sample standard deviation.

\( SE \) - standard error.

\( CI \) - confidence interval.

\( CL \) - confidence level.